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An Improved Local RBF Collocation Method for 3D Excavation Deformation Based on Direct Method and Mapping Technique

by Cheng Deng1,2, Hui Zheng2,*, Liangyong Gong1, Rongping Zhang1, Mengqi Wang3

1 Technology Center, Zhongheng Construction Group Co., Ltd., Nanchang, 330200, China
2 School of Infrastructure Engineering, Nanchang University, Nanchang, 330031, China
3 Zienkiewicz Centre for Computational Engineering, Swansea University, Swansea, SA2 8PP, UK

* Corresponding Author: Hui Zheng. Email: email

(This article belongs to the Special Issue: New Trends on Meshless Method and Numerical Analysis)

Computer Modeling in Engineering & Sciences 2025, 142(2), 2147-2172. https://doi.org/10.32604/cmes.2025.059750

Abstract

Since the plasticity of soil and the irregular shape of the excavation, the efficiency and stability of the traditional local radial basis function (RBF) collocation method (LRBFCM) are inadequate for analyzing three-dimensional (3D) deformation of deep excavation. In this work, the technique known as the direct method, where the local influence nodes are collocated on a straight line, is introduced to optimize the LRBFCM. The direct method can improve the accuracy of the partial derivative, reduce the size effect caused by the large length-width ratio, and weaken the influence of the shape parameters on the LRBFCM. The mapping technique is adopted to transform the physical coordinates of a quadratic-type block to normalized coordinates, in which the deformation problem can easily be solved using the direct method. The stability of the LRBFCM is further modified by considering the irregular shape of 3D excavation, which is divided into several quadratic-type blocks. The soil’s plasticity is described by the Drucker-Prager (D-P) model. The improved LRBFCM is integrated with the incremental method to analyze the plasticity. Five different examples, including strip excavations and circular excavations, are presented to validate the proposed approach’s efficiency.

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APA Style
Deng, C., Zheng, H., Gong, L., Zhang, R., Wang, M. (2025). An improved local RBF collocation method for 3D excavation deformation based on direct method and mapping technique. Computer Modeling in Engineering & Sciences, 142(2), 2147–2172. https://doi.org/10.32604/cmes.2025.059750
Vancouver Style
Deng C, Zheng H, Gong L, Zhang R, Wang M. An improved local RBF collocation method for 3D excavation deformation based on direct method and mapping technique. Comput Model Eng Sci. 2025;142(2):2147–2172. https://doi.org/10.32604/cmes.2025.059750
IEEE Style
C. Deng, H. Zheng, L. Gong, R. Zhang, and M. Wang, “An Improved Local RBF Collocation Method for 3D Excavation Deformation Based on Direct Method and Mapping Technique,” Comput. Model. Eng. Sci., vol. 142, no. 2, pp. 2147–2172, 2025. https://doi.org/10.32604/cmes.2025.059750



cc Copyright © 2025 The Author(s). Published by Tech Science Press.
This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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